Let $f(x) = -7x^{2}-10x+4$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}-10x+4 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = -10, c = 4$ $ x = \dfrac{+ 10 \pm \sqrt{(-10)^{2} - 4 \cdot -7 \cdot 4}}{2 \cdot -7}$ $ x = \dfrac{10 \pm \sqrt{212}}{-14}$ $ x = \dfrac{10 \pm 2\sqrt{53}}{-14}$ $x =\dfrac{5 \pm \sqrt{53}}{-7}$